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Asked by adititiwari601 25th June 2022, 1:23 PM
Answered by Expert
Answer:
begin mathsize 14px style A with rightwards arrow on top equals space 6 space i with hat on top space plus space 6 space j with hat on top space minus space 3 space k with hat on top end style
begin mathsize 14px style B with rightwards arrow on top equals space 7 space i with hat on top space plus space 4 space j with hat on top space plus space 4 space k with hat on top end style
angle θ between  begin mathsize 14px style A with rightwards arrow on top end style and begin mathsize 14px style B with rightwards arrow on top end style is given as
begin mathsize 14px style cos theta space equals space fraction numerator A with rightwards arrow on top times B with rightwards arrow on top over denominator open vertical bar A with rightwards arrow on top close vertical bar space space open vertical bar B with rightwards arrow on top close vertical bar end fraction end style
begin mathsize 14px style A with rightwards arrow on top times B with rightwards arrow on top equals space 42 plus 24 minus 12 space equals space 54 end style
 
begin mathsize 14px style open vertical bar A with rightwards arrow on top close vertical bar space equals space square root of 36 plus 36 plus 9 end root space equals 9 end style
 
begin mathsize 14px style open vertical bar B with rightwards arrow on top close vertical bar space equals space square root of 49 plus 16 plus 16 end root space equals 9 end style
 
cosθ = 54 /81 = 2/3
 
begin mathsize 14px style sin theta space equals space square root of 1 minus cos squared theta end root space equals space square root of 1 space minus space open parentheses 2 over 3 close parentheses squared end root space equals fraction numerator square root of 5 over denominator 3 end fraction end style
begin mathsize 14px style theta space equals space sin to the power of negative 1 end exponent open parentheses fraction numerator square root of 5 over denominator 3 end fraction close parentheses end style
Answered by Expert 25th June 2022, 2:09 PM
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